It's a 'volley gun' of some sort but it ain't a Nock. I didn't know that anybody else made any. Nock made a few hundred for the British Navy but they weren't well received. The idea was to carry them into the fighting tops and fire down on the enemy ship's crew. The problem was lighting off 6 or 7 .50 caliber musket barrels at once shove a man off balance and right off the fighting top.
Henry Nock gave the cluster of barrels on his a round profile.
jtg is right, it looks like a Volley gun of some sort.
Unlike the pepperbox guns which were supposed to fire individually (but not always ) those things would blast all barrels together. I have shot a double barrel 12 ga shot gun both barrels just to see what it would do (ouch). I can't imagine firing that thing!
Officially, it may be a volley gun but, unofficially, it has to be a pain in the ass to both load AND clean.
But, since it is a blackpowder gun, technically, I don't think you would even have to transfer it through an FFL, much less register it under NFA.
(However, NFA restrictions are over and above the definitions of C&R. You could, technically, have something that is old enough to fall under C&R, but if it were full-auto, it would still be illegal unless it has been properly registered and transferred via Class 3 dealer.)